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Mathematics

An express train makes a run of 240 km at a certain speed. Another train whose speed is 12 km/h less takes an hour longer to cover the same distance. Find the speed of the express train.

Quadratic Equations

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Answer

Let speed of express train be x km/hr, speed of other train will be (x - 12) km/hr.

Given,

Difference in time in covering 240 km between both the trains is 1 hour.

∴240x−12−240x=1⇒240x−240(x−12)x(x−12)=1⇒240x−240x+2880=x(x−12)⇒2880=x2−12x⇒x2−12x−2880=0⇒x2−60x+48x−2880=0⇒x(x−60)+48(x−60)=0⇒(x+48)(x−60)=0⇒x+48=0 or x−60=0⇒x=−48 or x=60.\therefore \dfrac{240}{x - 12} - \dfrac{240}{x} = 1 \\[1em] \Rightarrow \dfrac{240x - 240(x - 12)}{x(x - 12)} = 1 \\[1em] \Rightarrow 240x - 240x + 2880 = x(x - 12) \\[1em] \Rightarrow 2880 = x^2 - 12x \\[1em] \Rightarrow x^2 - 12x - 2880 = 0 \\[1em] \Rightarrow x^2 - 60x + 48x - 2880 = 0 \\[1em] \Rightarrow x(x - 60) + 48(x - 60) = 0 \\[1em] \Rightarrow (x + 48)(x - 60) = 0 \\[1em] \Rightarrow x + 48 = 0 \text{ or } x - 60 = 0 \\[1em] \Rightarrow x = -48 \text{ or } x = 60.

Since, speed cannot be negative.

∴ x = 60 km/hr.

Hence, speed of express train = 60 km/hr.

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